%I A158823
%S A158823 1,3,1,6,2,2,10,3,4,3,15,4,6,6,4,21,5,8,9,8,5,28,6,10,12,12,10,6,36,7,
%T A158823 12,15,16,15,12,7,45,8,14,18,20,20,18,14,8,55,9,16,21,24,25,24,21,16,9,
%U A158823 66,10,18,24,28,30,30,28,24,18,10,78,11,20,27,32,35,36,35,32,27,20,11,
               91
%N A158823 Triangle read by rows: matrix product A004736 * A158821.
%F A158823 sum_{m=1..n} T(n,m) = A000292(n).
%F A158823 T(n,m) = sum_{k=m..n} A004736(n,k)*A158821(k-1,m-1).
%F A158823 T(n,m) = A003991(n-1,m-1), m>1. [R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), 
               Oct 22 2009, Oct 30 2009]
%e A158823 First few rows of the triangle =
%e A158823 1;
%e A158823 3, 1;
%e A158823 6, 2, 2;
%e A158823 10, 3, 4, 3;
%e A158823 15, 4, 6, 6, 4;
%e A158823 21, 5, 8, 9, 8, 5;
%e A158823 28, 6, 10, 12, 12, 10, 6;
%e A158823 36, 7, 12, 15, 16, 15, 12, 7;
%e A158823 45, 8, 14, 18, 20, 20, 18, 14, 8;
%e A158823 55, 9, 16, 21, 24, 25, 24, 21, 16, 9;
%e A158823 66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10;
%e A158823 78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
%e A158823 91, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12;
%p A158823 A004736 := proc(n,m) n-m+1 ; end:
%p A158823 A158821 := proc(n,m) if m = 0 then 1; elif m = n then n; else 0; fi; 
               end:
%p A158823 A158823 := proc(n,m) add( A004736(n,k)*A158821(k-1,m-1),k=1..n) ; end: 
               seq(seq(A158823(n,m),m=1..n),n=1..8) ;
%Y A158823 Cf. A158821, A000292
%Y A158823 Sequence in context: A055151 A104573 A010467 this_sequence A122913 A069115 
               A065275
%Y A158823 Adjacent sequences: A158820 A158821 A158822 this_sequence A158824 A158825 
               A158826
%K A158823 nonn,tabl,easy,new
%O A158823 1,2
%A A158823 Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Mar 28 2009
%E A158823 Maple program added by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), 
               Oct 22 2009
%E A158823 Corrected A-number in a formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 30 2009